Before Calgary-born Kiesza Ellestad found her vocation as an amiable pop-house belter, she was a navy reservist who played folk songs to pass the time on voyages. Rechristened Kiesza, and on the up after hitting No 1 with one of this year’s biggest-selling singles, Hideaway, she now has a fund of anecdotes that reflect the way her life has changed.

“Somebody told me there was a video online of someone dancing to my song,” she tells us. “So I looked on Instagram, and I thought I recognised the person. It was Madonna.” There are whoops and high-fives on the dancefloor, and she bulldozes into the propulsive, bleepy Hideaway. It’s easy to see why Madge bestowed her blessings: Kiesza’a staccato dance moves and aerated vocals are the nearest thing 2014 offers to Paradise Garage-era Madonna. Attended by two dancers and dressed for comfort in a sports bra and wipe-clean PVC leggings, she affects a kind of time-travel experience that also takes in 90s house and rave – a medley of Robin S’s Show Me Love, Crystal Waters’s Gypsy Woman and Madonna’s own Vogue illustrates her infatuation with the high-drama dance-pop of the time. The title track of her new album, Sound of a Woman, is a balladeering blast similar to Lisa Stansfield’s All Woman, delivered with the same intensity, eyes clamped shut and dancing feet briefly stilled.

The odd slow track aside, the set is uptempo and packed with earwormy hooks. No Enemiesz threatens to offend spelling teachers everywhere and become a hit when it’s released this month; singing its Eurodisco-ish refrain brings her to such a pitch that her high voice is taut with the strain. Or maybe it’s just the strain of being a next-big-thing: “I’ve only had two days off since January,” she tells us, flopping on to the drum riser. A fan hurls a cowboy hat at the stage and she brightens. Slapping it on, she throws herself back into the business of raising the roof.